Research in AI4Science has shown promise in many science applications, including polymer design. However, current LLMs are ineffective in this problem space because: (i) most models lack polymer-specific knowledge, and (ii) existing aligned models have limited coverage of knowledge and capabilities relevant to polymer design. Addressing this, we introduce PolyBench, a large-scale training and test benchmark dataset of more than 125K polymer design-related tasks, leveraging a knowledge base of more than 13 million data points obtained from experimental and synthetic data sources to ensure broad coverage of polymers and their properties. For effective alignment using PolyBench, we introduce a knowledge-augmented reasoning distillation method that augments this dataset with structured CoT. Furthermore, tasks in PolyBench are organized from simple to complex analytical reasoning problems, enabling generalization tests and diagnostic probes across the problem space. Experiments show that small- and mid- sized language models (SLMs) with 7B to 32BB parameters, trained on PolyBench, outperform similar-sized models and remain competitive with closed-source frontier LLMs on PolyBench's test dataset, while demonstrating performance gains on external polymer benchmarks. Dataset and associated code available at https://github.com/StonyBrookNLP/PolyBench.