After many decades of study, the subject of the glass transition still has the power to engage, frustrate, and generate disagreement. However, its role as an important diagnostic means that a portion of this significant literature is focused less on how to understand the fundamentals of the transition, and more on how to predict its shift as conditions change. Within that body of work the question of composition dependence has attracted widespread interest, which is the focus of this Editorial. Two papers will be highlighted here, each representing important progress, particularly in the context of its time; they are separated by roughly a quarter of a century. Both describe binary mixtures, with extensions to more components being possible, and both occupy a “sweet spot” wherein a simple model expression, allied with a manageable number of characteristic parameters, allows for flexible experimental application. The first is “A Classical Thermodynamic Discussion of the Effect of Composition on Glass-Transition Temperatures” by Couchman and Karasz,(1) which dates from 1978. By that point, there had already been several decades of reference to the cryptic 1956 American Physical Society conference abstract by T. G. Fox,(2) giving the highly cited eponymous (parameter-free) equation for the glass transition of a “copolymer or plasticized polymer”, viz.(1)This prediction, that the inverse T_g of a mixture is just the mass fraction (w) weighted sum of the inverse pure component T_g values, is still widely used. As usual for the simplest relationship with predictive ambitions in a field, it only works well under very narrowly prescribed circumstances, for example, in the case of a polymer blend where the component T_g values are close and there are no strong inter- or intramolecular interactions. Note that the Fox equation connects inverse temperatures and thus relates sensibly to the notion that there is a physical process motivating the glass transition which can be identified with some kind of activation energy, e.g., a local motion, for which a rate law could be written that involves both an energetic barrier and the influence of local environment, e.g., through the bulk composition. This equation is usually not predictive, and it often fails to connect experimentally measured dots in a satisfying way. However, it can still be a useful approximation where a mixture T_g serves as input into a model for other aspects of mixture behavior. Alternative empirical relationships followed. In 1977 a number of these were summarized by Gordon et al.,(3) who collected a set of expressions that described T_g for a mixture in terms of pure component values weighted by mass or mole fractions, each involving an adjustable parameter. This was to be determined by fitting experimental composition–T_g data for the mixture of interest. The Gordon et al.(3) work focused on mixtures of organic small molecules and salts that behaved as regular solutions. The authors showed that the T_g mixture expressions could each be derived using the “configurational entropy theory” of Gibbs and DiMarzio,(4,5) which posits that cooling a glass-forming melt infinitely slowly results in a (hypothetically) second-order transition at a limiting temperature which is below the experimentally observed glass transition temperature. This temperature is identified with a vanishing configurational entropy for the system. In contrast to the statistical treatment of Gibbs–DiMarzio, Gordon et al.(3) approached the configurational entropy problem from a macroscopic experimental point of view using heat capacities to account for the temperature dependence of the relevant entropic contributions. They derived an expression for the composition dependence of the limiting temperature of the mixture and then assumed the same functional form for the composition dependence of the mixture’s glass transition temperature. Couchman and Karasz(1) were motivated by the Gordon et al.(3) work to shift even farther toward a classical thermodynamic treatment. In their paper, submitted just three months after the Gordon et al. paper appeared in print, the authors provided two derivations for the composition dependence of a mixture T_g using continuity arguments applied to classical thermodynamic functions, also assuming that the transition could be treated as a second-order Ehrenfest transition. Their first derivation followed an entropy route, with the authors taking the pure component entropies for each component to be continuous across the respective glass transitions and also taking the excess entropy of mixture to be continuous across the analogous mixture transition. This led to the following result for T_g of a mixture having mole fraction x₁ of component 1 (with pure T_g1) and x₂ of component 2 (with pure T_g2)(2)where ΔC_p represents the change in heat capacity for the component in going from the glassy to the rubbery state; all ΔC_p values are assumed to be independent of T. The authors noted that this result (eq 4 in their paper) was formally identical to the Gordon et al. form.(3) Couchman and Karasz(1) then went on to derive a second result for T_g of the mixture (their eq 5) by applying the assumption that the excess volume on mixing is also continuous across the glass transition. Concentrations were expressed in volume fractions (ϕ°), determined through pure component molar volumes taken at the glass transition. In this case the characteristic material quantity becomes the difference in thermal expansion coefficients (Δα, also taken to be independent of T) between the glassy and rubbery states for each component.(3) Ten years after the Couchman and Karasz paper was published, a related paper(6) appeared in this journal that included a very clear numerical comparison between the Couchman–Karasz prediction and those of Gordon et al., Fox, and others. Interestingly, the authors pointed out that, assuming T_g1 and T_g2 to be close and taking ΔC_p1 = ΔC_p2, the Fox equation can be derived from the original Couchman–Karasz result. Couchman and Karasz identified the two most likely sources of discrepancy between their results and experiment as being (i) failure of the assumption that ΔS_mix and/or ΔV_mix are continuous across T_g and (ii) nontrivial T dependence in ΔC_p or Δα. Insofar as the latter goes, the authors suggested that the assumed constant values could be replaced by using differences in the standard polynomial expressions that have been used for C_p and α—a reasonable suggestion, given that relevant coefficients have been tabulated for a wide variety of substances. With respect to the former point, the authors noted out that if both their eqs 4 and 5 were valid, it would lead to a constraint that links ΔC_p and Δα for a given component. This is analogous to what is known as the Prigogine–Defay ratio and has turned out to be an issue of some debate. McKenna(7) has a clear description of the criterion, which centers on the need for simultaneous satisfaction of volume and entropy continuity across the glass transition. If satisfied, the transition is considered to be truly second order. Some authors(8) cite evidence that this necessary condition does not hold. Others(9) observe that slightly relaxing the absolute condition on the Prigogine–Defay ratio yields the practical advantage of treating the transition as effectively second order and also creates a diagnostic that points to whether temperature (entropy) or density (volume) fluctuations are more dominant at the glass transition. In this context, McKenna(7) makes the interesting case that a rigorous test of the Prigogine–Defay condition would be extremely challenging because it would require determining characteristic physical properties of a substance following multiple paths, while requiring the same thermal and pressure histories as well as the same kinetics. Stepping back from such questions, we return to the fundamental point that made the Couchman and Karasz paper one of the subjects of this Editorial: It is a very highly cited work, as illustrated (red points) in Figure 1. Citations built up modestly in the initial years after it was published, but for the past 25 years they have appeared at a fairly constant rate. Accrual of over 600 citations suggests that concerns about entropy and volume continuity across the glass transition do not weigh heavily on many of the authors who refer to this paper. In fact, perusal of the citing literature reveals connection to a significant body of research involving the food and preservative industry. Figure 1. Citations per year and (inset) total citation numbers plotted against year for Couchman–Karasz(1) (red symbols) and Lodge–McLeish(11) (blue symbols). A fascinating glimpse into the complexity of that field is offered in a review article called “The Science of Food Structuring” by van der Sman and van der Goot.(10) The authors describe how tools from the soft matter community can be applied to understanding and controlling complex structures in food. Among their observations are that “The construction of food structuring diagrams requires some quantitative knowledge of glass and phase transitions ...” and “The glass transitions are often well described by the Couchman–Karasz relation.”(11) It is instructive to combine this with the comment from an earlier paper(6) that many experimental T_g–composition results can be well fit by the Couchman–Karasz expression—which captures the monotonic, nonlinear trends commonly observed—if one or both inputs for ΔC_p are treated as adjustable parameters. We will return to this point below. The second paper of interest is “Self-Concentrations and Effective Glass Transition Temperatures in Polymer Blends” by Lodge and McLeish, published in 2000.(12) The focus of this paper reflected growing interest in both the different dynamic responses of the components in a binary mixture and the breadth of their glass transitions. Back in 1982, Lau et al.(13) had reported on a differential scanning calorimetry (DSC) study of a series of miscible blends of polystyrene (PS) with poly(α-methylstyrene) (PαMS). Results showed the width of the blend glass transitions to be about triple that for the homopolymers. The authors suggested that “this broadening results from concentration inhomogeneities on the scale of the number of mobile units involved in the motion ...” and that “... connectedness in one dimension along the chain provides the main reason ... sufficient to cause a glass transition broadening.” As an interesting aside, they also concluded that the various available equations expressing the composition dependence of blend T_g did not do well, with one exception: the Couchman–Karasz equation (alas, attributed to Couchman, alone), but only if corrected for the temperature dependence of ΔC_p. By roughly a decade later the range of experimental methods applied to the study of blends had expanded, allowing for a more quantitative look at differences in behavior between the two components. For example, Chung et al.(14,15) used 2D deuteron exchange NMR to study a series of polyisoprene (PI)/poly(vinylethylene) (PVE) blends at temperatures near the glass transitions to characterize the composition dependence of segmental dynamics. The T_g–composition trends for PI and for PVE differed, and neither showed the composition dependence of the DSC-determined (single) blend T_g. The authors linked the observed dynamic heterogeneities to local compositional variation and, in statistical modeling to account for that, incorporated local compositional bias arising from chain connectivity to the central segment. Another finding was that the mobility distribution grew broader for both components as the amount of (higher T_g) PVE increased, which the authors connected to their observed broadening of the glass transition. In the same year, Zetsche and Fischer(16) applied dielectric relaxation methods to study the composition dependence of the α relaxation in PS/poly(vinyl methyl ether) (PVME) blends. They argued that a distribution of local compositions around a segment would lead to a local distribution of glass transitions, yielding the kind of broadened blend glass transition observed experimentally. Further, they identified the composition distribution as arising from composition fluctuations expected within a characteristic volume around a segment of interest; they connected this to the “cooperatively rearranging domain”.(16) This set the stage for the elegant contribution by Lodge and McLeish in 2000.(11) These authors outlined a very simple model that yielded quantitative predictions for the concentration of the neighborhood around a monomer of a given type and directly linked that to a composition-dependent effective glass transition for that component in the blend. This local concentration was identified as the “effective concentration”, φ_eff, and it differed from the bulk concentration, φ, because of local enrichment in like monomers due to chain connectivity. The result was quantified as a contribution of φ_self to the neighborhood, with the remainder filled using the bulk composition, φ. Thus(4)Lodge and McLeish provided a very clear route to φ_self: They prescribe the volume, V, of a local neighborhood as being directly proportional to l_K³, the cube of the Kuhn length, l_K, for the polymer of interest. Unlike the cooperatively rearranging domain(16) referred to above, this volume is expected to be only weakly temperature dependent. The ratio of the volume displaced by a Kuhn length strand to the neighborhood volume, V, gives the estimate of φ_self. While their calculation for φ_self was unambiguous, and while all necessary material-dependent information was provided in their paper for the systems studied, this author has sadly concluded, from work in multiple contexts, that it is a long and bumpy journey to track down values for most key polymer-dependent properties of interests, unless dealing with one of the usual suspects (for example, those “drosophila” of polymers, PS and PVME). Lodge and McLeish also showed that an effective concentration around a monomer of a given type would lead directly to an effective glass transition, T_g^eff, by applying any reasonable relationship that connected blend T_g to composition, i.e., by using T_g^eff(φ) = T_g(φ)|_φ=φeff. To keep things simple, they used the Fox equation for T_g(φ). With these steps Lodge and McLeish created a model for predicting component environment and glass transitions in polymer mixtures. Their approach provided a picture for how local environment controls local dynamic response. It also explicitly dealt with the case of a miscible blend exhibiting two glass transitions, the existence of which had been (and still sometimes is) taken as a signature of mixture immiscibility. Indeed, the Couchman–Karasz approach takes a single T_g as a given in a miscible mixture. Further, it provided a rationale for explaining observations such as the asymmetric nature of DSC traces in blends with components having significantly different T_g values, although, since it did not account for local composition fluctuations, it did not directly predict the extent of broadening. As the blue points in Figure 1 illustrate, very soon after publication papers citing this work appeared, and these rapidly accrued in number. Researchers soon(17−21) weighed in on whether the self-concentration approach, and the focus on a region determined roughly by the Kuhn length, led to insightful analysis of experimental and simulation data. None of these assessments challenged the underlying physical concepts nor, indeed, the generalities of the Lodge–McLeish approach. However, there was practical recognition that tethering the self-concentration volume to the Kuhn length did not always lead to optimal agreement between the model and experimental results. Lodge and McLeish, themselves, noted that “This definition could easily be modified by a multiplicative constant of order unity ...” but that such an adjustment “... would not affect the more qualitative effects”. In 2004 Lutz et al.(19) used ¹³C NMR to study the dynamics of polyisoprene (PI) blended with three other polymers and compared the Lodge–McLeish model prediction for φ_self of PI to the values obtained by optimizing agreement with their experimental data. Their fit values for φ_self turned out to depend on the blending partner, with results ranging from roughly 50–200% of the model calculation. In a later paper these authors(22) turned to PS solutions and concluded that a value of φ_self = 0.35 (compared to the original Lodge–McLeish calculation of 0.27) did very well when the component T_g values differed by more than 20 K. The need to be flexible in regards to φ_self is illustrated in Figure 2, reproduced from a 2006 study by Lipson and Milner(12) in which they revisited the Lodge–McLeish approach, as applied to polymer solutions. These authors introduced a model that led to predictions about both the composition dependence of DSC transitions and their broadening due to composition fluctuations, which Lodge and McLeish had not described. Lipson and Milner’s work connected with experimental data on PS in a number of solvents, but the results in Figure 2 focus on comparing Lodge–McLeish model predictions with experimental DSC results for PS–dibutyl phthalate (DBP) solutions reported by Savin et al.(23) For the solvent DBP the expectation would be φ_self = 0, so φ_eff = φ, i.e., the overall composition of the solution. Figure 2a shows that the Lodge–McLeish predictions for PS (dotted; φ_self = 0.35) and DBP (dashed; φ_self = 0) did not align very well with the experimental data (PS, triangles; DBP, squares). In Figure 2b we see that treating φ_self as an adjustable parameter met with greater success. Capturing the DBP results was possible with φ_self = 0.42, while the PS data required a very small (0 or 0.1) self-concentration. This implied that the local environment around a PS segment should be close to that of the global (bulk) average and also that T_g(PS) would be reasonably well predicted by the Fox equation. Figure 2. Component glass transition temperatures as a function of composition for a mixture of polystyrene (triangles) and dibutyl phthalate (DBP, squares). Symbols represent experimental data of Savin et al.(23) In (a) the short dashed curve is the Lodge–McLeish prediction for PS using φ_self = 0.35, and the long dashed curve is the prediction for DBP using φ_self = 0. In (b) the three upper curves are Lodge–McLeish predictions for T_g(PS) using φ_self = 0 (solid), 0.1 (long dash), and 0.2 (short dash); the lower curve is the prediction for T_g(DBP) using φ_self = 0.42. Reproduced with permission from ref (12). Copyright 2006 Wiley. Lipson and Milner outlined two major contributions in their treatment: the first required careful construction of a Bethe lattice model to predict how the breadth of DSC transitions related to composition fluctuations and size of local volume filled. The second introduced a “self-consistent” version of the Lodge–McLeish model. The authors observed that the composition pool from which the remaining neighbors of a central (polymer) segment are drawn had been depleted of monomer (because of the segment’s connected neighbors). Their self-consistent formulation accounted for that in filling the rest of the neighborhood and therefore satisfied the global composition average. They provided illustrative results in their paper, and this concept was also taken up in work by other researchers that followed; we will return to this point below. Figure 1 shows that much work has, indeed, followed publication of the original Lodge–McLeish paper. Numerous authors have concluded that the model is very useful in analyzing data on miscible blends, particularly when the components do not exhibit notable dynamic asymmetry. Rather than attempt to summarize this growing literature, we will touch on two studies in which the authors stated a clear goal of testing the self-concentration model of Lodge–McLeish for the more challenging case of polymer–small molecule mixtures. In 2008 Zheng and Simon(24) studied mixtures of PαMS and its oligomers, reasoning that concentration fluctuations—which are not accounted for in Lodge–McLeish—would be minimized in these athermal solutions. They found that fitting the model to their data yielded φ_self values significantly smaller than predicted. Taking their results in the context of previous work in the literature led them to speculate that local concentration effects might not, in the end, be strongly influenced by chain connectivity, but instead be dominated by component interactions and/or concentration fluctuations. Finally, a 2018 study by Yan and Wang(25) used rheological measurements on concentrated solutions of three polymers (PS and two polyolefins) in different solvents in order to extract effective glass transition temperatures for the polymers as well as φ_eff and φ_self. In addition to their own data, the authors plotted experimental results for φ_eff, obtained via optimizing φ_self, from a number of solution studies, comparing those both to Lodge–McLeish predictions and to predictions using Self-Consistent Lodge–McLeish. They concluded that using the original model formulation overestimated the importance of self-concentration around a polymer segment; they found that the self-consistent modification helped but did not completely address the issue. In summary, the papers by Couchman and Karasz and by Lodge and McLeish share a strong citation record, but what do they really have in common? The easy answer is a focus on the composition dependence of the glass transition in polymer mixtures. But there is another way to think about this question, and the answer provides a cautionary tale for theorists. Both papers use clean and very well-defined physical concepts; they develop models that incorporate significant approximations in the service of yielding simple, closed-form expressions for quantities of experimental interest that can be tested directly. The expressions contain characteristic material properties that can be specified independently by using measurable quantities. This is very satisfying. But, in the end, those material properties have essentially been turned by experimentalists into fitting functions in the service of analyzing data that do not yield to the originally defined metrics. From a theorist’s point of view, this might be somewhat of a disillusioning outcome, but all is not lost: An ungainly application method can be tolerated if the model still ends up revealing useful insight. The two papers highlighted here have each helped to illuminate the underlying physics in extended families of systems, and both richly deserve their citation status. Views expressed in this editorial are those of the author and not necessarily the views of the ACS. The author is grateful for the support of the National Science Foundation, Division of Materials Research, through Grant DMR-1708542. She also acknowledges useful conversations with Scott Milner and Ron White. This article references 25 other publications.

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混合物中玻璃过渡的全局和局部视图

经过数十年的研究，玻璃化转变的主题仍然具有参与，挫败和产生分歧的能力。但是，它作为重要的诊断工具的作用意味着，这一重要文献中的一部分较少集中在如何理解过渡的基本原理上，而更多地集中在如何预测随着条件变化而发生的变化。在该工作范围内，构成依赖性问题引起了广泛的关注，这是本社论的重点。这里将重点强调两篇论文，每篇论文都代表了重要的进展，特别是在其时代背景下；它们相距大约四分之一世纪。两者都描述了二元混合物，可能扩展了更多的组件，并且都占据了一个“甜蜜点”，其中简单的模型表达式，结合可管理数量的特征参数，可以灵活地进行实验应用。第一个是Couchman和Karasz撰写的“关于成分对玻璃化转变温度的影响的经典热力学讨论”，（1）始于1978年。到那时，已经有几十年的历史提到了1956年的神秘美国物理学家。 TG Fox的社会会议摘要，（2）给出了“共聚物或增塑的聚合物”的玻璃化转变的引人注目的同义（无参数）方程。（1）这种预测，即混合物的逆T _g只是逆纯组分T _g值的质量分数（ w）加权和，仍在广泛使用。通常，对于最简单的与预测性目标的关系而言，它仅在非常狭窄的规定条件下才能很好地发挥作用，例如，在聚合物共混物的情况下，组分T _g值接近且分子间或分子内不存在强相互作用互动。请注意，Fox方程连接了逆函数温度，因此与以下概念明智地相关：存在一个物理过程来激发玻璃化转变，可以通过某种活化能（例如局部运动）来识别该过程，为此可以编写速率定律，该定律涉及高能势垒和当地环境的影响，例如通过散装成分。该方程通常不是预测性的，并且通常无法以令人满意的方式连接实验测量的点。但是，当混合物T _g用作混合物行为其他方面的模型的输入时，它仍然可能是有用的近似值。随之而来的是替代的经验关系。1977年，Gordon等人（3）总结了其中的一些，他们收集了一组描述T _g的表达式。对于混合物，以纯组分值（按质量或摩尔分数加权）的方式表示，每个参数都包含一个可调参数。这可以通过拟合目标混合物的实验组成– T _g数据来确定。Gordon等人（3）的工作集中在有机小分子和盐的混合物上，这些混合物表现为常规溶液。作者表明，T _g可以使用Gibbs和DiMarzio（4,5）的“构型熵理论”推导每种混合物的表达式，该理论认为，无限缓慢地冷却形成玻璃的熔体会导致（假设地）在极限温度下发生二阶跃迁。低于实验观察到的玻璃化转变温度。用该系统消失的结构熵识别该温度。与Gibbs–DiMarzio的统计处理相反，Gordon等人（3）从宏观实验的角度出发，使用热容来解释相关熵贡献的温度依赖性，从而解决了结构熵问题。他们得出了混合物极限温度与组成的关系式，然后对混合物的玻璃化转变温度与组成的关系取相同的函数形式。Couchman和Karasz（1）受到Gordon等人（3）的推动，他们的工作甚至进一步转向了经典的热力学方法。在他们的论文中，戈登等人发表仅三个月。论文发表在印刷品上，作者针对混合物的成分依赖性提供了两个推导T _g使用适用于经典热力学函数的连续性参数，还假定该转变可以视为二阶埃伦菲斯特转变。他们的一阶推导遵循一条熵路线，作者将每种组分的纯组分熵在各自的玻璃化转变温度下保持连续，并将混合物的过量熵在类似混合物的跃迁状态下保持连续。这导致了以下结果为Ť_克具有摩尔分数的混合物的X ₁的组件1（用纯Ť _G1）和X ₂的组分2（用纯Ť _G2）（2）其中Δ Ç _p表示用于在从玻璃态向橡胶态去该组件的热容量的变化; 所有Δ Ç _p值被假设为独立的Ť。作者指出，这一结果（他们的论文中的等式4）与Gordon等人在形式上完全相同。（3）Couchman和Karasz（1）然后继续得出T _g的第二个结果通过假设混合时的过量体积在整个玻璃化转变过程中也是连续的，来确定混合物（方程式5）。浓度以体积分数（ϕ°）表示，通过玻璃化转变时的纯组分摩尔体积确定。在这种情况下，特征材料量变为每种组分的玻璃态和橡胶态之间的热膨胀系数之差（Δα，也与T无关）。（3） Couchman and Karasz论文发表十年后，相关期刊（6）出现在该期刊上，其中包括Couchman-Karasz预测与Gordon等人，Fox等人的预测之间非常清晰的数值比较。有趣的是，作者指出，假设T_G1和Ť _G2接近并采取Δ Ç _{p 1} =Δ Ç _{p 2}，Fox方程式可以推导从原始Couchman-Karasz结果。假设的Couchman和Karasz确定了他们的结果和实验之间的差异的两个最可能的来源为（ⅰ）失败即Δ小号_混合和/或Δ V_混合是跨越连续Ť_克和（ii）非平凡Ť在Δ依赖Ç _p或Δα。就后者而言，作者建议可以通过使用已用于C _p和α的标准多项式表达式中的差异来代替假定的常数值，这是一个合理的建议，因为已将多种不同的相关系数列表化物质。相对于前点，作者指出的是，如果他们两个方程4和5是有效的，这会导致链接Δ约束C ^ _p给定分量的Δα。这类似于所谓的Prigogine-Defay比，事实证明这是一些争论的问题。McKenna（7）对该标准进行了清晰的描述，该标准集中在同时满足玻璃跃迁的体积和熵连续性的需求上。如果满意，则认为过渡是真正的二阶。一些作者（8）援引证据表明这种必要条件不成立。其他人（9）观察到稍微放宽Prigogine-Defay比的绝对条件可产生将过渡有效地处理的实际优势第二阶，并且还会创建一个诊断，指出温度（熵）或密度（体积）的波动在玻璃化转变时是否更为明显。在这种情况下，McKenna（7）提出了一个有趣的案例，即严格测试Prigogine-Defay条件将极具挑战性，因为这将需要确定遵循多条路径的物质的特征物理特性，同时要求与以及相同的动力学。回避这些问题，我们回到使Couchman和Karasz论文成为本社论主题之一的基本观点：这是一个被高度引用的工作，如图1所示（红色点）。出版的最初几年，但在过去的25年中，它们以相当稳定的速度出现。引用次数超过600的结果表明，有关玻璃过渡过程中熵和体积连续性的担忧并未对许多参考本文的作者造成重大影响。实际上，对引用文献的阅读揭示了与涉及食品和防腐剂行业的大量研究的联系。图1. Couchman–Karasz（1）（红色符号）和Lodge–McLeish（11）（蓝色符号）的年度引文和（插入）总引文数与年份的关系图。van der Sman和van der Goot在一篇名为“食品结构的科学”的评论文章中，对该领域的复杂性有了一个令人着迷的瞥见。（10）作者描述了如何将软物质界的工具应用于理解和控制食品中的复杂结构。他们的观察结果是“构建食物结构图需要一定数量的玻璃和相变知识...”和“玻璃化转变通常由Couchman-Karasz关系很好地描述。”（11）结合起来很有启发性这与早期论文（6）的评论相吻合Ť_克组成-的结果可以是深受Couchman-Karasz表达-其捕获单调的，非线性的趋势通常观察到的，如果一个或两个输入，用于Δ适合Ç _p被视为可调参数。我们将在下面返回到这一点。感兴趣的第二篇论文是Lodge和McLeish于2000年发表的“聚合物共混物中的自浓度和有效玻璃化转变温度”。（12）本文的重点反映了人们越来越关注组件中不同组分的动态响应。二元混合物及其玻璃化转变的宽度。早在1982年，Lau等人（13）就通过差示扫描量热法（DSC）研究了一系列聚苯乙烯（PS）与聚（α-甲基苯乙烯）（PαMS）的可混溶共混物。结果表明，共混物玻璃化转变的宽度约为均聚物的三倍。作者认为，“这种扩大是由于运动中涉及的移动单元数量规模上的浓度不均匀性所致……”和“ .. 。沿链条的一维连通性是主要原因……足以引起玻璃化转变变宽。” 除了有趣的是，他们还得出结论，各种可用的方程式表示了混合物的成分依赖性Ť_克没有做好，但有一个例外：所述Couchman-Karasz方程（唉，归因于Couchman，单独的），但仅当校正Δ的温度依赖性Ç _p。大约十年后，用于共混物研究的实验方法范围扩大了，从而可以更定量地观察这两种组分之间的行为差​​异。例如，Chung等人（14,15）使用2D氘核交换NMR在接近玻璃化转变温度的条件下研究了一系列聚异戊二烯（PI）/聚（乙烯基乙烯）（PVE）共混物，以表征分段动力学的成分依赖性。的Ť_克– PI和PVE的成分趋势不同，均未显示DSC测定的（单一）混合物T _g的成分依赖性。作者将观察到的动态异质性与局部组成变化联系起来，并在统计建模中考虑到这一点，并入了由于链连接至中心链段而引起的局部组成偏差。另一个发现是随着（T _g的增加）PVE增加，这与他们观察到的玻璃化转变的扩大有关。同年，Zetsche和Fischer（16）应用介电弛豫方法研究了PS /聚（乙烯基甲基醚）（PVME）共混物中α弛豫的成分依赖性。他们认为，一个片段周围局部成分的分布会导致玻璃化转变的局部分布，从而产生一种通过实验观察到的变宽的混合玻璃化转变。此外，他们确定构图分布是由于在感兴趣的片段周围的特征体积内预期的构图波动引起的；他们将其与“合作重组领域”联系起来。（16）这为Lodge和McLeish在2000年做出的杰出贡献奠定了基础。混合物中该组分的有效玻璃化转变。这种局部浓度被确定为“有效浓度”，φ _EFF，并且它从本体浓度，φ不同，因为在像由于链连接单体局部富集。结果被量化为φ的贡献_自于附近，与使用批量组合物，φ填充剩余部分。因而（4）洛奇和麦克利什提供了非常明确的路线φ_自：他们规定的体积，V，局部邻域的作为是直接正比于升_ķ ³，库恩长度的立方，升_ķ，用于目标聚合物。与上面提到的协作重排域（16）不同，该体积仅受温度的影响很小。由库恩长度链的附近体积，排出的体积的比率V，给出φ的估计_自我。而他们对φ_自我的计算毫无疑问，尽管在他们的论文中为所研究的系统提供了所有必要的与材料相关的信息，但笔者可悲地断定，从多种情况下的工作出发，要追踪大多数关键聚合物的价值是漫长而坎bump的旅程，除非与通常的犯罪嫌疑人之一（例如，那些聚合物，PS和PVME的“果蝇”）打交道，否则它取决于利益。小屋和麦克利什还表明，围绕一个给定类型的单体的有效浓度将直接导致有效的玻璃化转变，Ť_克^EFF，通过应用连接共混物的任何合理的关系Ť_克的组合物，即通过使用Ť_克^EFF（ φ）= T _g（φ）| _{φ = φ EFF}。为简单起见，他们将Fox方程用于T _g（φ）。通过这些步骤，Lodge和McLeish创建了一个预测聚合物混合物中组分环境和玻璃化转变的模型。他们的方法为本地环境如何控制本地动态响应提供了一张图片。它也明确地处理了具有两种玻璃化转变的可混溶共混物的情况，该过渡的存在已被（有时仍然被）视为混合物不可混溶的标志。实际上，Couchman–Karasz方法仅需一个T _g作为给定的可混溶混合物。此外，它为解释观察结果提供了原理，例如与具有显着不同的T _g的组分共混的DSC痕迹的不对称性质。但是，由于没有考虑局部成分的波动，因此无法直接预测扩大幅度。如图1中的蓝点所示，引用该工作的出版物发表后不久，这些出版物的数量迅速增加。研究人员很快（17-21）权衡了是否采用自我集中方法以及对库恩长度大致确定的区域的关注，从而对实验和模拟数据进行了深刻的分析。这些评估都没有挑战基本的物理概念，也没有挑战Lodge-McLeish方法的一般性。但是，实际上已经认识到，将自我浓缩量绑定到库恩长度并不总是导致模型与实验结果之间的最佳一致性。Lodge和McLeish自己 指出“该定义可以很容易地通过阶数为...的乘法常数来修改”，但是这样的调整“ ...不会影响更多的定性效果”。在2004年，Lutz等人（19）使用了¹³ C NMR研究的聚异戊二烯（PI）的动态混合与其它三种聚合物并比较φ洛奇-麦克利什模型预测_自PI的通过与他们的实验数据优化协议获得的值。他们对φ拟合值_自横空出世，取决于混合伙伴，结果从模型计算的约50-200％。在后面的纸张这些作者（22）转向PS解决方案并得出结论认为φ的值_自= 0.35（相对于0.27的原始洛奇-麦克利什计算）的表现非常好当组分Ť_克值相差超过20开尔，有必要在关于φ灵活的_自如图2所示，图2摘自Lipson和Milner（12）2006年的一项研究，在该研究中，他们重新审视了应用于聚合物溶液的Lodge-McLeish方法。这些作者介绍了一个模型，该模型可以预测DSC过渡的组成依赖性以及由于组成波动而引起的扩展，而Lodge和McLeish并未对此进行描述。Lipson和Milner的工作与多种溶剂中PS的实验数据相关，但图2中的结果集中于比较Savin等人报道的Lodge-McLeish模型预测与PS-邻苯二甲酸二丁酯（DBP）溶液的DSC实验结果。 23）对于溶剂DBP的预期是φ_自我= 0，所以φ _EFF=φ，即溶液的整体成分。图2a示出的是，旅馆-麦克利什预测为PS（虚线;φ_自我= 0.35）和DBP（虚线;φ_自我= 0）不对齐很好与实验数据（PS，三角形; DBP，正方形）。在图2b我们看到，治疗φ_自我为会见了更大的成功可调参数。捕获DBP结果是可能的，φ_自我= 0.42，而PS数据所需的非常小的（0或0.1）自浓度。这意味着PS段周围的局部环境应接近全球（总体）平均值，并且T _g（PS）由Fox方程可以很好地预测。图2.聚苯乙烯（三角形）和邻苯二甲酸二丁酯（DBP，正方形）混合物的组分玻璃化转变温度与组成的关系。符号表示的的Savin等人。（23）在（a）中的实验数据的短虚线曲线是使用φ洛奇-麦克利什预测PS_自= 0.35，和长虚线曲线是使用φ为DBP预测_自我= 0。在（b）中的三个上部曲线是洛奇-麦克利什预测为Ť_克使用φ（PS）_自我= 0（实线），0.1（长划线）和0.2（短划线）; 下部曲线是用于预测Ť_克使用φ（DBP）_自= 0.42。经参考文献（12）许可复制。版权所有2006 Wiley。利普森（Lipson）和米尔纳（Milner）概述了他们的治疗方法中的两个主要贡献：第一个需要仔细构建贝特格子模型，以预测DSC跃迁的宽度如何与成分波动和填充的局部体积有关。第二个版本引入了Lodge-McLeish模型的“自洽”版本。作者观察到，从中抽取出中心（聚合物）链段的其余邻居的成分池中的单体已经耗尽（因为该链段相连的邻居）。他们自洽的表述解决了其余社区的填充问题，因此满足了全球平均构成。他们在论文中提供了说明性的结果，此概念随后也被其他研究人员采纳。我们将在下面返回到这一点。图1表明，Lodge–McLeish原始论文的发表确实有很多工作。许多作者得出结论，该模型在分析可混溶共混物的数据时非常有用，尤其是当组分没有明显的动态不对称性时。我们不会尝试总结这些不断增长的文献，而是会涉及两项研究，其中作者提出了一个明确的目标，即针对更具挑战性的聚合物-小分子混合物的情况测试Lodge-McLeish的自我浓缩模型。Zheng和Simon（24）在2008年研究了PαMS及其低聚物的混合物，认为在这些无热溶液中，浓度波动（在Lodge-McLeish中没有考虑）将被最小化。_自我价值明显小于预期。在文献中先前工作的背景下得出他们的结果，使他们推测，局部浓度效应最终可能不会受到链连接性的强烈影响，而是受到组分相互作用和/或浓度波动的支配。最后，（25）2018年研究通过严和王使用，以提取针对所述聚合物的有效玻璃化转变温度以及φ上在不同溶剂三种聚合物（PS和两种聚烯烃）的浓溶液流变学测量_EFF和φ_自我。除了自己的数据，作者绘制φ实验结果_EFF，通过优化φ获得_自我，从许多解决方案研究中，将它们与Lodge-McLeish预测以及使用自洽Lodge-McLeish的预测进行比较。他们得出结论，使用原始模型公式高估了聚合物片段周围自浓缩的重要性。他们发现自洽的修改有帮助，但并未完全解决该问题。总之，Couchman和Karasz的论文以及Lodge和McLeish的论文有着很强的引用记录，但它们的真正共同点是什么？简单的答案是关注聚合物混合物中玻璃化转变的成分依赖性。但是还有另一种思考这个问题的方式，答案为理论家们提供了一个警示。这两篇论文都使用了干净且定义明确的物理概念。他们开发了一些模型，这些模型结合了明显的近似值，从而产生了可以直接测试的大量实验兴趣的简单，封闭形式的表达式。这些表达式包含可以通过使用可测量量独立指定的特征材料特性。这是非常令人满意的。但是，最后，这些材料属性实际上已被实验人员转换为拟合函数，以服务于无法得出原始定义指标的数据分析。从理论家的角度来看，这可能是一个令人幻想破灭的结果，但一切都不会丢失：如果该模型最终仍显示出有用的见识，则可以容忍一种笨拙的应用方法。此处重点介绍的两篇论文均有助于阐明系统扩展家族中的基础物理学，并且都应得到应有的引用。本社论中表达的观点只是作者的观点，不一定是ACS的观点。作者感谢美国国家科学基金会材料研究部通过Grant DMR-1708542提供的支持。她还感谢与Scott Milner和Ron White进行的有益对话。本文引用了其他25个出版物。她还感谢与Scott Milner和Ron White进行的有益对话。本文引用了其他25个出版物。她还感谢与Scott Milner和Ron White进行的有益对话。本文引用了其他25个出版物。